Attitude measurement method

ABSTRACT

An attitude measurement method, which relates to the technical field of measurement while drilling in directional drilling, which can improve the observability of inertial instrument errors, suppress the repeatability errors of gyroscopes and improve the attitude measurement accuracy. The method adopts the method of fine alignment at multiple positions to carry out initial alignment; the method includes the steps of: S1, taking current attitude data and velocity data of the strapdown inertial navigation system as first initial values, and performing fine alignment at a first position; S2, changing the position of a strapdown inertial navigation system to an nth position, and performing attitude update and velocity update according to the last fine alignment result in the position changing process; and S3, taking the results of attitude update and velocity update as the nth initial values, performing the nth fine alignment at the nth position to complete the initial alignment of the strapdown inertial navigation system, thereby realizing attitude measurement. The solution of the present invention is suitable for measuring the horizontal attitude and azimuth of the whole inclined section of a horizontal well, especially the application of directional drilling gyro measurement while drilling in the attitude measurement of large inclined wells and horizontal wells.

FIELD

The present invention relates to the technical field of directionaldrilling attitude measurement, in particular to an attitude measurementmethod for large inclined wells and horizontal wells and a directionaldrilling gyro measurement while drilling method.

BACKGROUND

At present, with the gradual extension of the world exploration field tocomplex areas and special environments, the development difficulty andcost will greatly increase. The exploration and development situationpromotes the evolution and development of well types, and the proportionof wells with complex structures such as extended reach wells,ultra-thin reservoir horizontal wells and multi-branch wells in oil andgas field exploration and development is increasing. With thedevelopment of steerable drilling technology represented by rotarysteering technology, especially for applications in deep and ultra-deepsteerable drilling, the requirements for well trajectory controlaccuracy are constantly improving.

The demands for advanced gyroscopes in oil exploration and developmentare that: gyroscopes that meet the requirements for high temperature andstrong vibration and have a small volume and a high precision havealways been the unswerving pursuit of the inertial technology in the oilindustry. Especially in the case of interference of fluxgate duringdirectional drilling, it is not that there is no need for gyroscopes atpresent, but rather there is no suitable gyroscope product which canwork normally for a long time in harsh environments such as a hightemperature and strong vibration. As to a gyroscope-related technologyapplied in steerable drilling, the reliability in harsh environment isan important basis for selection, so it is necessary to develop a kindof attitude measurement method that can meet the requirements for themost demanding use scenarios in the field of oil drilling survey, tosolve the problems of environmental adaptability under high temperatureand strong vibration environments, and bias repeatability.

The existing calibration methods only start from the differences inexternal environment interference suppression ability, calculationamount and other perspectives, and do not consider the large drift errorof inertial instrument caused by the specific use environment for GyroMeasurement while Drilling (GMD), i.e., harsh environment such as a hightemperature and strong vibration. However, the actually existing drifterror of inertial instrument will affect the calibration accuracy ofexisting calibration methods. Under the harsh environment of a hightemperature and strong vibration, the bias repeatability error is themain bottleneck restricting the accuracy of a gyroscope.

Therefore, it is necessary to develop an attitude measurement method todeal with the shortcomings of the prior art, so as to solve or alleviateone or more of the above problems and improve the construction accuracyof well trajectory.

SUMMARY

In view of the above, the present invention provides an attitudemeasurement method, which has the ability of fault tolerance andalignment under slight sloshing, and can improve the observability ofinertial instrument errors without changing the precision of theinertial instrument itself, and suppress the repeatability error of thegyroscope when started successively, thus improving the accuracy ofattitude measurement.

In one aspect, the present invention provides an attitude measurementmethod, used for a strapdown inertial navigation system, whereinrepeatability drift of a gyroscope is suppressed by adopting a method ofperforming fine alignment at a plurality of positions respectively;

the method includes the steps of:

S1, taking current attitude data and velocity data of the strapdowninertial navigation system as first initial values, and performing firstfine alignment at a first position;

S2, changing the position of the strapdown inertial navigation system toan nth position, and performing attitude update and velocity updateaccording to a result of an (n−1)th fine alignment in an positionchanging process; and

S3, taking results of the attitude update and velocity update as nthinitial values, and performing an nth fine alignment at the nth positionto complete an initial alignment of the strapdown inertial navigationsystem;

wherein, n is incremented by 1 from 2, and steps S2 and S3 are repeateduntil n=k; k is the number of positions selected by the method, and k isgreater than or equal to 2.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: the plurality of positions are specificallytwo positions, i.e., k=2.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: the fine alignment is realized by Kalmanalgorithm.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: the fine alignment using Kalman algorithmcomprises: time update and/or measurement update;

the time update refers to completing update of a state variableaccording to real-time data collected by the system, including attitudeupdate and velocity update;

the measurement update refers to correcting an error of a state updatewith measurement data to realize optimal estimation.

The Kalman filter uses a velocity measurement after zero-speedcorrection and an angular rate measurement constrained by the earthrotation angular rate for the measurement update and optimal estimation,so as to improve alignment accuracy.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: when the method is used for drillingmeasurement, the data of initial value of the fine alignment includes awell inclination angle, a tool face angle and an azimuth angle.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: the measurement update includes the steps of:

1) judging whether a measurement data value is valid, if the measurementdata value is valid, entering step 2), otherwise, performing no update,and taking a result of the time update as a final result of the Kalmanfilter; and

2) updating a result of the state update according to the measurementdata value, calculating a gain coefficient according to an updatingresult and the result of the time update to obtain optimal stateestimation.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: judging whether the measurement data value isvalid is realized by judging whether a drill collar is in a static stateand/or whether external disturbance meets an alignment requirement; ifthe drill collar is in the static state and/or the external disturbancemeets the alignment requirement, it is determined that the measurementdata value is valid, otherwise it is determined that the measurementdata value is invalid.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: judging whether the drill collar is in thestatic state specifically comprises: judging whether a sensing-velocityobservation value and/or a sensing-angular-rate observation value isless than a judgment threshold; if the sensing-velocity observationvalue and/or the sensing-angular-rate observation value is less than thejudgment threshold, judging that the drill collar is in the staticstate; otherwise, judging that the drill collar is not in the staticstate.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: judging whether the external disturbancemeets the alignment requirement specifically comprises: judging whethera disturbance amount of external mud or a vibration amount sensed by avibration sensor is less than a set threshold value; if the disturbanceamount of external mud or the vibration amount sensed by the vibrationsensor is less than the set threshold value, judging that the externaldisturbance amount meets the alignment requirement, otherwise judgingthat the external disturbance amount does not meet the alignmentrequirement;

the specific values of the thresholds in the above judgment conditionsare determined according to the actual conditions such as the drillinggeological environment and depth.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: the sensing-velocity observation value is areal-time acceleration value of the gyroscope; the sensing-angular-rateobservation value is a root mean square value of the angular rate of thegyroscope.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: the step 2) specifically comprises: accordingto a sequential processing method, respectively solving a measurementequation composed of a velocity measurement Z_(V) after zero-speedcorrection and an angular rate measurement Z_(ω) constrained by theearth rotation angular rate, so as to realize constant drift erroroptimal estimation of X and Y horizontal gyroscopes and constant drifterror estimation of a Z-axis gyroscope, and finally complete optimalestimation of an attitude and an azimuth misalignment angle.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: one-step state prediction and one-step meansquare error prediction are completed during the time update.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: the attitude update in the position changingprocess is carried out by a quaternion method.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: the measurement method further comprisescoarse alignment at the first position, and performs the first finealignment using a result of the coarse alignment as the first initialvalues.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: the Kalman state equation is specifically:

{dot over (X)}=FX+W

where,

${F = \begin{bmatrix}0_{3 \times 3} & {f^{n} \times} & 0_{3 \times 3} & C_{b}^{n} \\0_{3 \times 3} & {{- \omega_{ie}^{n}} \times} & {- C_{b}^{n}} & 0_{3 \times 3} \\0_{3 \times 3} & 0_{3 \times 3} & 0_{3 \times 3} & 0_{3 \times 3} \\0_{3 \times 3} & 0_{3 \times 3} & 0_{3 \times 3} & 0_{3 \times 3}\end{bmatrix}},{W = \begin{bmatrix}{C_{b}^{n}\nabla_{w}^{b}} \\{{- C_{b}^{n}}ɛ_{w}^{b}} \\0_{3 \times 1} \\0_{3 \times 1}\end{bmatrix}}$

∇_(w) ^(b) and ε_(w) ^(b) are random white noises of the accelerometerand gyroscope in a body coordinate system, respectively; C_(b) ^(n) isthe attitude transition matrix of a navigation coordinate system and thebody coordinate system; X and {dot over (X)} represent Kalman filterstate variables;

X=[(δv ^(n))^(T)(ϕ^(n))^(T)(ε₀ ^(b))^(T)(∇₀ ^(b))^(T)]^(T),

ω_(ie) ^(n)=[0ω_(ie) cos Lω _(ie) sin L]^(T);

δv^(n) is the velocity error, Φ^(n) is the mathematical platformmisalignment angle of strapdown inertial navigation, ε₀ ^(b) is theconstant drift of the gyroscope, ∇₀ ^(b) is the constant bias of theaccelerometer; ω_(ie) the angular rate of earth rotation; L is latitude;T represents the transposition of the matrix;

ƒ^(n)=[0 0 g], g is the acceleration of gravity;

the attitude transition matrix C_(b) ^(n) of the navigation coordinatesystem and the body coordinate system is as follows:

${C_{b}^{n} = \begin{bmatrix}{{\cos{\psi cos}}_{\gamma} + {\sin{\psi sin\theta sin}}_{\gamma}} & {\sin{\psi cos\theta}} & {{\cos{\psi sin}}_{\gamma} - {\sin{\psi sin\theta cos}}_{\gamma}} \\{{- {\sin{\psi cos}}_{\gamma}} + {\cos{\psi sin\theta sin}}_{\gamma}} & {\cos\psi\cos\theta} & {{- {\sin{\psi sin}}_{\gamma}} - {\cos\psi\sin\theta\cos}_{\gamma}} \\{- {\cos{\theta sin}}_{\gamma}} & {\sin\theta} & {\cos{\theta cos}}_{\gamma}\end{bmatrix}},$

where, θ represents a pitch angle, ψ represents a yaw angle, and γrepresents a roll angle.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: the formula for the time update includes:

an equation for one-step state prediction:

{circumflex over (X)} _(k/k-1)=Φ_(k/k-1) {circumflex over (X)}_(k-1/k-1);

and an equation for one-step mean square error prediction:

P _(k/k-1)=Φ_(k/k-1) P _(k-1/k-1)Φ_(k/k-1) ^(T)+Γ_(k/k-1) Q_(k-1)Γ_(k/k-1) ^(T).

The above-mentioned aspect and any possible implementations furtherprovide an implementation: the formula used for update of velocitymeasurement is:

an equation for velocity measurement: Z_(v)=δv^(n)=H_(v)X+V_(v), where,

H _(v)=[I _(3×3)0_(3×3)0_(3×3)0_(3×3)].

The formula used for update of the earth rotation angular ratemeasurement is:

an equation for earth rotation angular rate measurement:

Z _(ω)=[0_(3×3)ω_(ie) ^(n) ×C _(b) ^(n)0_(3×3)]X+V _(ω);

where,

V_(v) is the velocity measurement noise in the navigation coordinatesystem;

V_(ω) is the angular rate measurement noise;

v^(n) is an output velocity, δv^(n) is a velocity error, and is used asmeasurement data, I is a unit matrix, Z_(ω) is an angular-rateobservation value and Z_(v) is a velocity observation value.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: the formula for calculating the gain of theKalman filter is:

Kalman filter gain equation (5.5):

K _(k) =P _(k/k-1) H _(k) ^(T)(H _(k) P _(k/k-1) H _(k) ^(T) +R _(k))⁻¹;

The formula for completing optimal attitude estimation is:

state estimation equation (5.6):

{circumflex over (X)} _(k/k) ={circumflex over (X)} _(k/k-1) +K _(k)(Z_(k) −H _(k) {circumflex over (X)} _(k/k-1)),

state estimation means square error equation (5.7):

P _(k/k)=(I−K _(k) H _(k))P _(k/k-1).

The above-mentioned aspect and any possible implementations furtherprovide an implementation: an Euler analytical method is used for thecoarse alignment on a static base, and calculation is carried outdirectly according to the data of the accelerometer and gyroscope.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: the formula for the coarse alignmentincludes:

Pitch Angle

{circumflex over (θ)}=a tan 2({tilde over (ƒ)}_(y),√{square root over({tilde over (ƒ)}_(x) ²+{tilde over (ƒ)}_(z) ²)}),

Roll Angle

{circumflex over (γ)}=a tan 2(−{tilde over (ƒ)}_(x),{tilde over(ƒ)}_(z)),

Yaw Angle

{circumflex over (ψ)}=a tan 2({tilde over (ω)}_(x) cos {circumflex over(γ)}+{tilde over (ω)}_(z) sin {circumflex over (γ)},{tilde over (ω)}_(x)sin {circumflex over (θ)} sin {circumflex over (γ)}+{tilde over (ω)}_(y)cos {circumflex over (θ)}−ω_(z) cos {circumflex over (γ)} sin{circumflex over (θ)});

where, {tilde over (ƒ)}_(x), {tilde over (ƒ)}_(y) and {tilde over(ƒ)}_(z) are the measurement data of a three-component acceleration onthe body, respectively. ({tilde over (ω)}_(x), {tilde over (ω)}_(y) and{tilde over (ω)}_(z) are the measurement data of a three-componentgyroscope on the body, respectively. The measurement data of thegyroscope mainly refers to the angular rate.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: the first Kalman alignment and the secondKalman alignment take less than 130 s, and the azimuth alignmentaccuracy for horizontal well can be achieved within 1 deg.

In another aspect, the present invention provides a measurement whiledrilling system, including a strapdown inertial navigation system whichincludes a triaxial gyroscope and a triaxial accelerometer; wherein thestrapdown inertial navigation system adopts any one of the attitudemeasurement methods as described above to suppress a repeatability drifterror of the gyroscope and improve accuracy of measurement whiledrilling in directional drilling.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: the gyroscope is a Coriolis vibratorygyroscope.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: the gyroscope is a high-temperature resonatorgyroscope;

the strapdown inertial navigation system also includes a shock absorberwhich is fixedly connected with the high-temperature resonatorgyroscope.

The above-mentioned aspect and any possible implementations furtherprovide an implementation: the high-temperature resonator gyroscopeincludes a resonator, a circuit board, piezoelectric ceramics, asupporting base, a shell and a binding post, wherein the resonator isarranged in the shell and connected with the supporting base; thepiezoelectric ceramics are connected with the binding post throughconductive metal wires; the circuit board realizes signal transmissionand performs fixed connection at key process points of internalcomponents of the gyroscope; the fixedly connected key process pointsare located between the piezoelectric ceramics and the resonator,between the binding post and the piezoelectric ceramics, between thebinding post and the circuit board, between the supporting base and theresonator, and between the shell and the supporting base.

In another aspect, the present invention provides a continuousnavigation measurement system, including a strapdown inertial navigationsystem which includes a triaxial gyroscope and a triaxial accelerometer;wherein the strapdown inertial navigation system adopts any one of theattitude measurement methods as described above to suppress arepeatability drift error of the gyroscope and improve attitudemeasurement accuracy in a navigation process.

Attitude measurement information, including a horizontal attitude angleand an azimuth angle, is three parameters: generally, a pitch angle (awell inclination angle) and a roll angle (a tool face angle) are calleda horizontal attitude, and a yaw angle (an alignment azimuth) is calledan azimuth angle. The purpose of the initial alignment is to perform therelated algorithm processing by collecting the data of the accelerometerand gyroscope in real time, so as to acquire the attitude information(the horizontal attitude angle and azimuth angle) of the body.

Compared with the prior art, the present invention can obtain thefollowing technical effects: when the interference angular rate causedby mud sloshing is greater than the earth rotation angular rate, thealignment method can still normally find north, has the better abilityof fault tolerance and alignment under slight sloshing, can improve theobservability of inertial instrument errors without changing theprecision of the inertial instrument itself, and realize the optimalestimation of inertial instrument errors thereby improving the initialalignment accuracy. The two-position alignment algorithm based on Kalmanoptimal estimation uses strapdown inertial navigation attitude updatealgorithm and velocity update algorithm to update the angular motion andlinear motion of the body in real time, and uses zero-velocity and/orearth rotation angular rate correction algorithm for measurement updateand optimal estimation, so that the optimal estimation accuracy isirrelevant to the accuracy of changing the position, and it is notnecessary to know the exact position of the position changing mechanism,which is very beneficial in engineering practice, thereby avoiding thedesign of complex stop structure and avoiding the use ofhigh-temperature-resistant angle measuring mechanism. Changing positionfor the drift error elimination or drift measurement can only realizedrift measurement of horizontal gyroscopes (i.e., X and Y gyroscopes),but cannot realize drift measurement of Z-axis gyroscopes under a largewell inclination angle. By providing constraint relationship throughzero-velocity correction and constant angular rate correction, the driftmeasurement of Z-axis gyroscopes can be realized especially.

Obviously, it is not necessary for any product of implementing thepresent invention to achieve all the above technical effects at the sametime.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to explain the technical solution of the embodiments of thepresent invention more clearly, the drawings used in the embodimentswill be briefly introduced below. Obviously, the drawings in thefollowing description are only some embodiments of the presentinvention, and for those skilled in the art, other drawings can beobtained according to these drawings without paying any creative labor.

FIG. 1 is a schematic diagram of bias elimination by changing a positionof a single-axis gyroscope according to an embodiment of the presentinvention.

FIG. 2 is a curve graph of misalignment angles of the alignment of asouth-north well trajectory during the two-position alignment (i.e.,position changing alignment) according to an embodiment of the presentinvention.

FIG. 3A is a curve graph of gyroscope constant drift estimation errorsof the south-north well trajectory during bias correction by a positionchanging method according to an embodiment of the present invention.

FIG. 3B is a curve graph of accelerometer constant drift estimationerrors of the south-north well trajectory during bias correction by aposition changing method according to an embodiment of the presentinvention.

FIG. 4 is a curve graph of misalignment angles of horizontal attitudeand azimuth alignment when the well trajectory runs east-west directionduring bias correction by a position changing method according to anembodiment of the present invention.

FIG. 5A is a curve graph of gyroscope constant drift estimation errorsof an east-west well trajectory during bias correction by a positionchanging method according to an embodiment of the present invention.

FIG. 5B is a curve graph of accelerometer constant drift estimationerrors of an east-west well trajectory during bias correction by aposition changing method according to an embodiment of the presentinvention.

FIG. 6 is a curve graph of full-well inclination azimuth alignmentaccuracies obtained under different constant drift errors by atwo-position bias correction method according to an embodiment of thepresent invention.

FIG. 7 is a flow chart of a two-position Kalman filter algorithmaccording to an embodiment of the present invention.

FIG. 8 is a flow chart of a sequential processing method of atwo-position Kalman algorithm according to an embodiment of the presentinvention.

FIG. 9 is a schematic diagram of a two-position+Kalman alignment processaccording to an embodiment of the present invention.

FIG. 10 is a curve graph of misalignment angle errors of a south-northwell trajectory during bias correction by a two-position+Kalmanalignment method according to an embodiment of the present invention.

FIG. 11A is a diagram of a gyroscope drift estimation error of asouth-north well trajectory during bias correction by atwo-position+Kalman alignment method according to an embodiment of thepresent invention.

FIG. 11B is a diagram of a gyroscope drift estimation error of asouth-north well trajectory during bias correction by atwo-position+Kalman alignment method according to an embodiment of thepresent invention.

FIG. 12 is a curve graph of misalignment angle errors of a vertical wellduring bias correction by a two-position+Kalman alignment methodaccording to an embodiment of the present invention.

FIG. 13A is a curve graph of gyroscope drift estimation errors in avertical well during bias correction by a two-position+Kalman alignmentmethod according to an embodiment of the present invention.

FIG. 13B is a curve graph of accelerometer drift estimation errors of avertical well during bias correction by a two-position+Kalman alignmentmethod according to an embodiment of the present invention.

FIG. 14A is a curve graph of small well inclination misalignment angleestimation errors of an east-west well trajectory during bias correctionby a two-position+Kalman alignment method according to an embodiment ofthe present invention.

FIG. 14B is a curve graph of large well inclination misalignment angleestimation errors of an east-west well trajectory during bias correctionby a two-position+Kalman alignment method according to an embodiment ofthe present invention.

FIG. 15A is a graph of a constant drift estimation error of a gyroscopeunder a large well inclination angle of 70° in an east-west welltrajectory during bias correction by a two-position+Kalman alignmentmethod according to an embodiment of the present invention.

FIG. 15B is a graph of a constant drift estimation error of anaccelerometer under a large well inclination angle of 70° in aneast-west well trajectory during bias correction by atwo-position+Kalman alignment method according to an embodiment of thepresent invention.

FIG. 16 is a simulation graph of a GMD alignment misalignment angleerror under a full well inclination angle in an east-west welltrajectory during bias correction by a two-position+Kalman alignmentmethod according to an embodiment of the present invention.

FIG. 17A is a curve graph of constant drift estimation errors of agyroscope under a full well inclination angle in an east-west welltrajectory during bias correction by a two-position+Kalman alignmentmethod according to an embodiment of the present invention.

FIG. 17B is a curve graph of constant drift estimation errors of anaccelerometer under a full well inclination angle in an east-west welltrajectory during bias correction by a two-position+Kalman alignmentmethod according to an embodiment of the present invention.

FIG. 18 is a schematic diagram of attitude measurement of a standardstrapdown inertial navigation system.

FIG. 19 is a schematic diagram of steerable drilling: a horizontal wellaccording to the present invention.

DETAILED DESCRIPTION

In order to better understand the technical solution of the presentinvention, embodiments of the present invention will be described indetail with reference to the accompanying drawings.

It should be clear that the described embodiments are only part of theembodiments of the present invention, not all thereof. Based on theembodiments of the present invention, all other embodiments obtained bythose skilled in the art without any creative labor belong to theclaimed scope of the present invention.

Terms used in the embodiments of the present invention are for thepurpose of describing specific embodiments only, and are not intended tolimit the present invention. As used in the embodiments of the presentinvention and the appended claims, the singular forms “a”, “the” and“this” are also intended to include the plural forms unless the contextclearly indicates other meaning.

In view of the shortcomings of the prior art, the attitude measurementmethod of the present invention adopts the method ofKalman+multi-position (especially two-position)+zero velocity tocalibrate a large well inclination angle and correct the constant biasof angular velocity. As shown in FIG. 19, a horizontal well includes: avertical (well) section, frontal distance from target point (inclinedwell section) and a horizontal (well) section, in which the wellinclination angle of the vertical section is defined as 0°, anddisplacement in front of target (the inclined well section) means asection where the well inclination angle is greater than 0° and lessthan 90°, which is usually divided into a small well inclination angle(e.g. 0-20°) and a large well inclination angle (e.g. greater than 70°),which are just commonly known in the field without clear definition. Thehorizontal section refers to the section where the well inclinationangle is 90°. The definition of full well inclination refers to coveringfrom the vertical section to the horizontal section, and the wellinclination angle is from 0° to 90°. Two-position is one of theimplementation solutions, and any position can be used in practice. Fromthe point of view of a mechanical structure design, two-positionalignment is convenient for mechanical structure design, that is,through the design of a mechanical stop, accurate two-point positioningcan be realized.

The deduction logic of the measuring method of the present invention isas follow:

1. Basic Principle of Gyro-Steering

Gyro-steering is based on the principle of Gyrocompass, which mainlyuses inertial devices (accelerometers and gyroscopes) to measure theangular rate vector of the earth rotation and the acceleration vector ofgravity, so as to calculate the included angle between the body and thegeographical north direction.

The angular rate ω_(ie) of the earth rotation is a fixed value of15.041067°/h (about 0.0042°/s), the longitude and latitude of thelocation where the measured body is are λ and L, respectively, andEast-North-Up geographic coordinate system is adopted.

According to the principle of gyro-steering, the horizontal component ofthe angular rate of the earth rotation is ω_(N), of which the magnitudedepends on the latitude L of the measuring location.

ω_(N)=ω_(ie) cos L  (1.1)

For example, the latitude of Beijing is 40°, and the horizontalcomponent of the earth rotation is about 11.52°/h. The higher thelatitude, the smaller the horizontal component, and the horizontalcomponent tends to zero near the pole position.

Assuming that the sensing axis of the gyroscope is in the same phase asthe moving direction of the body, and defining the azimuth angle ψ asthe included angle between the sensing axis of the gyroscope and thenorth direction, the output value of the gyroscope is obtained asfollows:

ω_(ab)=ω_(N) cos ψ+B=ω _(ie) L cos ψ+B  (1.2)

In equation (1.2), ω_(ob) is an output value of the gyroscope, that is,the observed value, B is the bias of the gyroscope.

By solving equation (1.2), the azimuth angle ψ of the body can becalculated. In addition, it can be seen from equation (1.2) that themeasurement data of the gyroscope contains the bias B of the gyroscopeitself, and its value may directly affect the calculation result of theazimuth angle, which is usually eliminated by multi-point positionchange or continuous rotation modulation. FIG. 1 shows the workingprinciple of a single-axis gyroscope by changing the sensing directionthrough the rotation of the position changing mechanism. In order tofacilitate the mechanical design of the position changing mechanism, asimple position changing method of two positions of 0° and 180° isadopted. The outputs of the gyroscope are respectively as follows:

ω_(ob)(0)=U ₁ /SF ₁=ω_(ie) cos L cos ψ+B ₁  (1.3)

ω_(ob)(180)=U ₂ /SF ₂=−ω_(ie) cos L cos ψ+B ₂  (1.4)

In equations (1.3) and (1.4), SF₁, SF₂, U₁, U₂, B₁ and B₂ respectivelyrefer to the scale factors, outputs (analog values or digital values)and bias of the gyroscope at 0° and 180° positions.

By setting the north-finding accuracy of the GMD to 1°, and ignoring thescale factor error of the gyroscope, the azimuth measurement of asingle-axis gyroscope can be estimated as follows from (1.3) and (1.4):

$\begin{matrix}{\hat{\psi} = {{\arccos\frac{{\omega_{ob}(0)} - {\omega_{ob}(180)}}{\omega_{N}{\cos\psi}}} = {\arccos\left( {{\cos\psi} + \frac{ɛ_{B}}{\omega_{N}{\cos\psi}}} \right)}}} & (1.5)\end{matrix}$

In equation (1.5), ε_(B) is the residual drift error after positionchanging compensation. Taking Taylor expansion of the above equation andignoring the high-order term, and the estimation error (precision) attwo positions is obtained as follows

$\begin{matrix}{{\delta\psi} \approx \frac{ɛ_{B}}{\omega_{N}{\sin\psi}}} & (1.6)\end{matrix}$

It can be seen from equation (1.6) that when a single gyro is used fortwo-position change, the estimation error is the smallest when the twochanged positions are selected near the east-west direction (ψ₁=90°,270°), and the estimation error at this time is:

$\begin{matrix}{{\delta\psi} = {\frac{ɛ_{B}}{\omega_{N}} = \frac{ɛ_{B}}{\omega_{ie}{\cos L}}}} & (1.7)\end{matrix}$

Equation (1.7) gives the basic formula of a north-finding estimationaccuracy error of the gyroscope. It can be seen that the north-findingaccuracy of two-position change is related to a residual drift error ofthe gyroscope and the local latitude.

2. Steering Principle (Initial Alignment Method)

The steering principle adopts an Euler angle analysis method, whichdirectly calculates the pitch angle (the well inclination angle) θ, rollangle (the tool face angle) γ and yaw angle (the azimuth angle) ψ of thebody by using information of the gyroscope and accelerometer. Beforegiving the analytic two-position alignment and two-position Kalmanoptimal estimation alignment solution parsed by the present invention,the principle and limit accuracy of a coarse alignment are given byusing the Euler angle analysis method.

Because the geographical location of the drilling location is known, thecomponent of the angular rate vector of the earth rotation in thegeographical coordinate system and the gravity vector can be accuratelyobtained at this time, as follows:

$\begin{matrix}{{\omega_{ie}^{n} = {\begin{bmatrix}0 \\{\omega_{ie}{\cos L}} \\{\omega_{ie}{\sin L}}\end{bmatrix} = \begin{bmatrix}0 \\\omega_{N} \\\omega_{U}\end{bmatrix}}},\begin{matrix}{g^{n} = \begin{bmatrix}0 \\0 \\{- g}\end{bmatrix}} & \;\end{matrix}} & (2.1)\end{matrix}$

in which, g, ω_(ie), and L represent the local gravity acceleration, theearth rotation angular velocity, and the local latitude, respectively.The north component of the earth rotation angular velocity is recordedas ω_(N)=ω_(ie) cos L, and the normal component of rotation angularvelocity of the earth is recorded as ω_(u)=ω_(ie) sin L.

In the process of a coarse alignment on a static base, the gyroscope andaccelerometer in a GMD system respectively measure the projections ofthe gravity vector and earth rotation angular rate in the bodycoordinate system. By ignoring the influence of mud sloshinginterference, the measurement data of a three-component gyroscope andthree-component acceleration on the body are as follows:

{tilde over (ω)}_(ie) ^(b) =Ĉ _(n) ^(b)ω_(ie) ^(n)  (2.2)

{tilde over (ƒ)}^(b) =−Ĉ _(n) ^(b) g ^(n)  (2.3)

where,

{tilde over (ω)}_(ib) ^(b)=[{tilde over (ω)}_(x){tilde over(ω)}_(y){tilde over (ω)}_(z)]^(T),{tilde over (ƒ)}^(b)=[{tilde over(ƒ)}_(x){tilde over (ƒ)}_(y){tilde over (ƒ)}_(z)]^(T)  (2.4)

The time for coarse alignment is generally very short, and the smoothingaverage values within a period of time are generally taken as themeasurement data values of inertial instruments. When inertialinstruments have no obvious drift errors of trend terms, the longer thesmoothing time, the better the accuracy can be obtained. Considering thecoarse alignment time and alignment accuracy comprehensively, thesmoothing time can be judged and analyzed by Allan variance test data,and the optimal time for smoothing is based on the time when Allanvariance “bottoms out”.

From equation (2.3), the pitch angle can be obtained:

{circumflex over (θ)}=a tan 2({tilde over (ƒ)}_(y),√{square root over({tilde over (ƒ)}_(x) ²+{tilde over (ƒ)}_(z) ²)})  (2.4)

The roll angle can be obtained:

{circumflex over (γ)}=a tan 2(−{tilde over (ƒ)}_(x),{tilde over(ƒ)}_(z))  (2.5)

On the basis of obtaining {circumflex over (θ)}, and {circumflex over(γ)}, they are substituted into equation (2.2) to obtain:

$\begin{matrix}{{\begin{bmatrix}{\cos\hat{\gamma}} & 0 & {\sin\hat{\gamma}} \\{\sin\hat{\theta}\sin\hat{\gamma}} & {\cos\hat{\theta}} & {{- \cos}\hat{\gamma}\sin\hat{\theta}} \\{{- \sin}\hat{\gamma}\cos\hat{\theta}} & {\sin\hat{\theta}} & {\cos\hat{\gamma}\cos\hat{\theta}}\end{bmatrix}\begin{bmatrix}{\overset{\sim}{\omega}}_{x} \\{\overset{\sim}{\omega}}_{y} \\{\overset{\sim}{\omega}}_{z}\end{bmatrix}} = \begin{bmatrix}{{- \sin}\hat{\psi}\omega_{ie}{\cos L}} \\{\cos\hat{\psi}\omega_{ie}{\cos L}} \\{\omega_{ie}{\sin L}}\end{bmatrix}} & (2.6)\end{matrix}$

The azimuth angle can be solved as:

{circumflex over (ψ)}=a tan 2({tilde over (ω)}_(x) cos {tilde over(γ)}+{tilde over (ω)}_(z) sin {tilde over (γ)},{tilde over (ω)}_(x) sin{circumflex over (θ)} sin {tilde over (γ)}+{tilde over (ω)}_(y) cos{circumflex over (θ)}−{tilde over (ω)}_(z) cos {tilde over (γ)} sin{circumflex over (θ)})  (2.7)

Equations (2.4), (2.5), and (2.7) constitute the basic algorithm of theEuler angle coarse alignment. The accuracy limit of the Euler analyticalmethod for static base alignment is analyzed below.

Considering the bias errors of the accelerometer and gyroscope:

∇^(n) =C _(b) ^(n)∇^(b)ε^(n) =C _(b) ^(n)ε^(b)  (2.8)

In equation (2.8), ∇^(b) and ∇^(n) respectively represent the biaserrors of the accelerometer in a body coordinate system and a navigationsystem, ε^(b) and ε^(n) respectively represent the bias errors of thegyroscope in a body coordinate system and a navigation system.

When solving the differential in one direction and making the angles inthe other two directions zero, the two sides of equations (2.4), (2.5)and (2.7) are differentiated respectively and the second-order smallitem is ignored to obtain:

$\begin{matrix}{\phi_{ɛ} = {{- {\delta\theta}} = {\frac{{\cos\theta}{\nabla_{y}{- {\sin\theta}}}\nabla_{z}}{g} = \frac{\nabla_{N}}{g}}}} & (2.9) \\{\phi_{N} = {{- {\delta\gamma}} = {\frac{{\cos\gamma}{\nabla_{x}{+ {\sin\gamma}}}\nabla_{y}}{g} = \frac{\nabla_{E}}{g}}}} & (2.10) \\{\phi_{U} = {{\delta\psi} = {{- \frac{{{\sin\psi}\left( {ɛ_{y} - {\delta\theta\omega}_{U}} \right)} + {{\cos\psi}\left( {ɛ_{x} + {\delta\gamma\omega}_{U}} \right)}}{\omega_{N}}} = {\frac{{- ɛ_{E}} + {\phi_{N}\omega_{U}}}{\omega_{N}} = {\frac{ɛ_{E}}{\omega_{N}} + {\frac{\nabla_{E}}{g}{\tan L}}}}}}} & (2.11)\end{matrix}$

Equations (2.9), (2.10) and (2.11) determine the accuracy limit ofstatic base alignment, that is, the formula of an analytical method forcoarse alignment, and the data of the accelerometer and gyroscope can bedirectly used for calculation. Attitude alignment accuracy under astatic base mainly depends on the drift error of the accelerometer ineast and north directions, while azimuth alignment accuracy mainlydepends on the drift error of the gyroscope in east direction and thedrift error of the accelerometer in east direction.

In Kalman optimal estimation, the superscript {circumflex over ( )}represents the estimated value, or the calculated value. If there is nosuperscript, it means that the value is a state value. For example, theestimated value of the well inclination angle θ is {circumflex over(θ)}.

In addition, the measurement data values of accelerometers andgyroscopes selected in equations (2.4), (2.5) and (2.7) can be obtainedin many ways. Generally, the average value, sampling time and limitaccuracy of sampled values for a period of time are selected, which areusually expressed by an Allan variance method, and the lowest point ofthe Allan variance is taken as the evaluation of an accuracy limit.Therefore, the longer the integration time, the higher the accuracyafter smoothing. However, when there is a trend term error or a drifterror, the length of the integration time depends on the time constantof the drift error. When there are abnormal data in the samplingprocess, or the unexpected disturbance of the drill collar at this time,the measurement error is brought, which is also the biggest risk andproblem of coarse alignment.

3. The Method and Principle of Eliminating Constant Bias by Changing thePosition Index (i.e., a Two-Position Bias Elimination Method)

The traditional method of eliminating a drift error and improvingazimuth alignment accuracy is to use position change index.

Assuming that the constant bias of inertial instrument is constantbefore and after changing the position, and ignoring the interference ofangular motion and linear motion before and after rotation, by rotatingthe Inertial Measurement Unit (IMU) around one direction, the attitudetransition matrix at two positions is constructed, and the observabilityof the constant bias is increased. In practical applications, limited bythe size of inertial instrument and the size characteristics of theslender rod of a GMD probe, the design of position changing mechanismcan only be around the axial direction of the probe, i.e., the directionof the input axis around the Z-axis gyroscope.

The positions before and after the position of the gyroscope is changedare b₁ and b₂, and the average values of sampling outputs ofcorresponding gyroscopes in alignment time are ω ^(b1) and ω ^(b2), andthe average values of sampling outputs before and after the position ofthe accelerometer is changed are ƒ ^(b1) and ƒ ^(b2), respectively.Assuming that the included angle between positions b₁ and b₂ is β, thenthe state transition matrix formed thereby is C_(b1) ^(b2),

$\begin{matrix}{C_{b_{1}}^{b_{2}} = \begin{bmatrix}{\cos\beta} & {- {\sin\beta}} & 0 \\{\sin\beta} & {\cos\beta} & 0 \\0 & 0 & 1\end{bmatrix}} & (3.1)\end{matrix}$

then, there is a relationship between outputs of the inertial instrumentat position b₁ and b₂:

ω^(b2) =C _(b) ₁ ^(b) ² ω^(b) ¹ ,ƒ^(b) ² =C _(b) ₁ ^(b) ² ƒ^(b) ¹  (3.2)

Considering that the time of position changing process is very short,ignoring the first-order Markov process in the random constant, andconsidering that the constant drift of inertial instrument is unchangedbefore and after changing the position, only the influence of the randomdrift is considered. In addition, because the gyroscope rotates around Zaxis, the sensing direction of a Z-axis gyroscope and accelerometer isunchanged before and after changing the position, so the separation ofthe Z-axis constant drift cannot be realized. When only the output of ahorizontal-axis inertial instrument is considered,

$C_{b_{1}}^{b_{2}} = \begin{bmatrix}{\cos\beta} & {- {\sin\beta}} \\{\sin\beta} & {\cos\beta}\end{bmatrix}$

According to equation (3.2), the output of a horizontal gyroscope atposition b₂ is:

$\begin{matrix}{\begin{bmatrix}{\overset{\_}{\omega}}_{x}^{b_{2}} \\{\overset{\_}{\omega}}_{y}^{b_{2}}\end{bmatrix} = {{C_{b_{1}}^{b_{2}}\begin{bmatrix}\omega_{x}^{b_{1}} \\\omega_{y}^{b_{1}}\end{bmatrix}} + \begin{bmatrix}ɛ_{0x} \\ɛ_{0y}\end{bmatrix} + \begin{bmatrix}{\overset{\_}{ɛ}}_{{xw}_{2}} \\{\overset{\_}{ɛ}}_{{yw}_{2}}\end{bmatrix}}} & (3.3)\end{matrix}$

Similarly, the output of a horizontal accelerometer at position b₂ canbe obtained as follows:

$\begin{matrix}{\begin{bmatrix}{\overset{\_}{f}}_{x}^{b_{2}} \\{\overset{\_}{f}}_{y}^{b_{2}}\end{bmatrix} = {{C_{b_{1}}^{b_{2}}\begin{bmatrix}f_{x}^{b_{1}} \\f_{y}^{b_{1}}\end{bmatrix}} + \begin{bmatrix}\nabla_{0x} \\\nabla_{0y}\end{bmatrix} + \begin{bmatrix}{\overset{\_}{\nabla}}_{{xw}_{2}} \\{\overset{\_}{\nabla}}_{{yw}_{2}}\end{bmatrix}}} & (3.4)\end{matrix}$

Equation (3.3) and equation (3.4) show that in theory, the constantdrift of horizontal inertial instrument can be separated at any tinyrotation angle β, and when the rotation angle β is 180°, det(I-C_(b1)^(b2)) is the largest, and the separation of the constant drift error isleast affected by the random drift. When the influence of the randomdrift in the position changing process is not considered, the estimatedvalue of the constant drift of the horizontal gyroscope is:

$\begin{matrix}\left\{ \begin{matrix}{{\hat{ɛ}}_{x} = {\frac{1}{2}\left( {{\overset{\_}{\omega}}_{x}^{b_{2}} + {\overset{\_}{\omega}}_{x}^{b_{1}}} \right)}} \\{{\hat{ɛ}}_{y} = {\frac{1}{2}\left( {{\overset{\_}{\omega}}_{y}^{b_{2}} + {\overset{\_}{\omega}}_{y}^{b_{1}}} \right)}}\end{matrix} \right. & (3.5)\end{matrix}$

The estimated value of the bias of the horizontal accelerometer is:

$\begin{matrix}\left\{ \begin{matrix}{{\hat{\nabla}}_{x}{= {\frac{1}{2}\left( {{\overset{\_}{f}}_{x}^{b_{2}} + {\overset{\_}{f}}_{x}^{b_{1}}} \right)}}} \\{{\hat{\nabla}}_{y}{= {\frac{1}{2}\left( {{\overset{\_}{f}}_{y}^{b_{2}} + {\overset{\_}{f}}_{y}^{b_{1}}} \right)}}}\end{matrix} \right. & (3.6)\end{matrix}$

The estimated value of the accelerometer after two-position calibrationis obtained as follows:

$\quad\left\{ \begin{matrix}{{\hat{f}}_{x}^{b} = {\frac{1}{2}\left( {{\overset{\_}{f}}_{x}^{b_{2}} - {\overset{\_}{f}}_{x}^{b_{1}}} \right)}} \\{{\hat{f}}_{y}^{b} = {\frac{1}{2}\left( {{\overset{\_}{f}}_{y}^{b_{2}} - {\overset{\_}{f}}_{y}^{b_{1}}} \right)}}\end{matrix} \right.$

The estimated value of the gyroscope after two-position calibration is:

$\quad\left\{ \begin{matrix}{{\hat{\omega}}_{x}^{b} = {\frac{1}{2}\left( {{\overset{\_}{\omega}}_{x}^{b_{2}} - {\overset{\_}{\omega}}_{x}^{b_{1}}} \right)}} \\{{\hat{\omega}}_{y}^{b} = {\frac{1}{2}\left( {{\overset{\_}{\omega}}_{y}^{b_{2}} - {\overset{\_}{\omega}}_{y}^{b_{1}}} \right)}}\end{matrix} \right.$

However, the Z-axis accelerometer and gyroscope are unobservable, so theaverage value before and after changing the position is directly takenas the estimated value after calibration:

$\quad\left\{ \begin{matrix}{{\hat{f}}_{z}^{b} = {\frac{1}{2}\left( {{\overset{\_}{f}}_{z}^{b_{2}} - {\overset{\_}{f}}_{z}^{b_{1}}} \right)}} \\{{\hat{\omega}}_{z}^{b} = {\frac{1}{2}\left( {{\overset{\_}{\omega}}_{z}^{b_{2}} + {\overset{\_}{\omega}}_{z}^{b_{1}}} \right)}}\end{matrix} \right.$

According to the estimated values of the gyroscope and accelerometerafter calibration, using the coarse alignment principle similar to thesingle-position Euler angle analysis, the inclination angle aftercalibration can be obtained as follows:

{circumflex over (θ)}=a tan 2({circumflex over (ƒ)}_(y) ^(b)({circumflexover (ƒ)}_(x) ^(b))²+({circumflex over (ƒ)}_(z) ^(b))²)  (3.7)

The tool face angle after calibration is:

{circumflex over (γ)}=a tan 2[−{circumflex over (ƒ)}_(x) ^(b),(−ƒ _(z)^(b) ² +ƒ _(z) ^(b) ¹ )](3.8)

The azimuth angle after calibration is:

{circumflex over (ψ)}=a tan 2({circumflex over (ω)}_(x) ^(b) cos{circumflex over (γ)}+{circumflex over (ω)}₂ ^(b) sin {circumflex over(γ)},{circumflex over (ω)}_(x) ^(b) sin {circumflex over (θ)} sin{circumflex over (γ)}+{circumflex over (ω)}_(y) ^(b) cos {circumflexover (θ)}−{circumflex over (ω)}₂ ^(b) cos {circumflex over (γ)} sin{circumflex over (θ)})  (3.9)

Equations (3.7)-(3.9) constitute the basic algorithm for analyzingtwo-position alignment by changing the position by 180° around the Zaxis.

Analyzing two positions solves the problem of constant drift errorcalibration of inertial instrument, and improves the alignment accuracy,especially the azimuth alignment accuracy. For small inclination anglemeasurement, the main alignment error comes from the error of positionchanging mechanism and the random drift error of inertial instrument.Because of the design of changing the position by 0-180°, only the finalpositioning accuracy of changing the position is concerned, which isconvenient for the design of position changing mechanism. In practicalapplications, the positioning accuracy of changing the position can beimproved and the design is simplified through the design of a stopstructure. With regard to the random drift error, assuming that thealignment time of each position is t, the random walk coefficient of thegyroscope is N=0.005 deg/√{square root over (h)}, then the statisticalmean square deviation in time t is obtained as σ=0.005 deg/√{square rootover (h)}/√{square root over (t)}. By setting the total alignment timeas 300 s, assuming that the alignment time of each position is 145 s,then the random error of the gyroscope caused accordingly is aboutε_(w)=0.017 deg/h. For a quartz flexible accelerometer with a noise of 2μg/√{square root over (Hz)}, the mean square value of random error is 20μg in the frequency band of 100 Hz. According to the analytical formula(2.11) of the Euler analytical method of azimuth alignment accuracylimit, the azimuth error caused by a random error can be calculated tobe about 0.1 deg by setting the latitude of 40° N. In the followingsimulation, a similar conclusion will be drawn.

For directional drilling measurement applications, under a large wellinclination angle and different trajectory directions, the accuracylimit and error mechanism that can be measured by the two-positionanalytical method are simulated and analyzed. The simulation process isas follows:

The error parameters of the gyroscope and accelerometer are set as thesimulation parameters of high-temperature inertial instrument inTable 1. The initial position is set to [116° E, 40° N, 100 m], and theinstrument is in the first alignment position in the first 145 s,rotates by 180° to the second position along the Z-axis direction of theprobe during 146-155 s, and then continues to align for 145 s, with thetotal alignment time of 300 s. The well inclination angle is in therange of 0-90°, one position is taken every 1°, there are 91 positionsin total, and 40 Monte-Carlo simulations are carried out for eachposition, and the root mean square value is taken.

TABLE 1 Simulation parameter setting table of high-temperature inertialinstrument Error source Error form Indicators Gyroscope Mean squaredeviation of [2; 2; 2]°/h repeatability drift random constant Gyrorandom noise Angle random walk [0.005; 0.005; 0.005]°/√h Accelerometerbias Mean square deviation of 200 μg repeatability random constantAccelerometer Mean square deviation of 2 μg/√Hz@DC − 100 Hz random noisenoise

Simulation 1: The well trajectory is south-north direction, and thevertical well attitude azimuth is [0°,0°,0°] and the horizontal wellattitude azimuth is [90°,0°,0°] in the geographic coordinate system.FIG. 2 is a curve of alignment misalignment angle errors, and FIG. 3(a)and FIG. 3(b) are the constant drift estimation errors of the gyroscopeand accelerometer in turn.

It can be seen from FIG. 2 that the azimuth alignment accuracy is notaffected by the well inclination angle when the well trajectory to bemeasured is in the south-north direction, that is, the azimuthmeasurement error is always around 0.1° from the vertical well sectionto the horizontal well section, which is also in line with theconclusion of formula (2.11). It is not difficult to understand from theinitial alignment mechanism that the azimuth misalignment angle isrelated to the accuracy of the equivalent east gyroscope, and since theeast gyroscope can always be changed the position and modulated from thevertical well section to the horizontal well section in the south-northdirection, that is, the constant drift of the east and west gyroscopescan always be observed, that is, the constant drift of the equivalenteast gyroscope can be eliminated under any well inclination angle bymeans of changing the position. The final azimuth alignment accuracymainly depends on the random drift of the east gyroscope. The simulationresults in FIG. 2 can verify this conclusion. In addition, it can beseen from the east misalignment angle in FIG. 2 and the estimation errorcurve of a Z-axis accelerometer in FIG. 3(b) that the observability ofthe Z-axis accelerometer becomes worse with the increase of theinclination angle, and when the Z-axis inclines in the south-northdirection, the error of the east misalignment angle increases with theincrease of the inclination angle, but its error is far less than thetarget accuracy index, and the influence can be ignored.

Simulation 2: The well trajectory runs the east-west direction. In thegeographic coordinate system, the vertical well attitude azimuthcoordinates are [0°,0°,90°], and the horizontal well attitude azimuthcoordinates are [90°,0°,90°]. The simulation results are shown in FIG.4.

It can be seen from FIG. 4 that when the well trajectory is in the eastdirection, the estimation error of the azimuth misalignment angleincreases obviously with the increase of the well inclination angle. Themain reason is that when the well inclination angle increases, theZ-axis gyroscope becomes the main contributor to the error of the eastgyroscope, while the position change rotates around the Z-axis, and theconstant drift of the Z-axis itself is unobservable, thus directlycausing the error of the azimuth misalignment angle. It can also be seenfrom FIG. 4 that in order to ensure that the azimuth measurementaccuracy is better than 1°, the well inclination angle cannot exceed10°.

For two-position analytical alignment, the azimuth measurement accuracyunder a large inclination angle can be improved by reducing the constantdrift of the gyroscope. FIG. 6 gives the simulation curves of azimuthmeasurement accuracy under different inclination angles of the gyroscopewith different constant drifts. It can be seen that the accuracyrequirement of well trajectory measurement is 1°, in order to ensure theaccuracy under a large well inclination angle, it is required that theconstant drift of the gyroscope to be less than 0.2 deg/h. For theworking conditions under high-temperature and strong-vibrationenvironment, the bias repeatability error is the main bottleneckrestricting the accuracy of the gyroscope. It is very challenging todevelop a gyroscope that meets the constant drift error of 0.2 deg/hunder working conditions.

For analytical two-position alignment, on the premise of fixed precisionof inertial devices, the azimuth accuracy of a small well inclinationangle under east-west trajectory and the full well inclination angle(0-90°) under south-north trajectory can be effectively improved bymeans of position changing calibration, but the azimuth accuracy of alarge well inclination angle under east-west trajectory still cannotmeet the use requirements, so a more effective method is needed toimprove the azimuth measurement accuracy of a large well inclinationangle under the condition of limited precision of inertial devices.

4. Alignment Method of Two-Position+Kalman

According to the present invention, a multi-position and Kalmanalignment method is adopted to solve the drift measurement problem ofthe east gyroscope under a large well inclination angle.

The method includes the following steps:

the navigation coordinate system is East-North-Up geographic coordinatesystem, a 12×1-dimension inertial navigation system precise alignmentmathematical model is established, and the state variables of the Kalmanfilter are as follows:

X=[(δv ^(n))^(T)(ϕ^(n))^(T)(ε₀ ^(b))^(T)(∇₀ ^(b))^(T)]^(T)  (4.1)

In equation (4.1): δv^(n) is a velocity error, Ø^(n) is a mathematicalplatform misalignment angle of strapdown inertial navigation, ε₀ ^(b) isa constant drift of a high-temperature gyro, ∇₀ ^(b) is a constant biasof a high-temperature accelerometer; ε₀ ^(b) and ∇₀ ^(b) are mainlycaused by the repeatability error of successive start-up of the hightemperature inertial instruments. According to the error model of thestrapdown inertial navigation system under a static base and by ignoringa small amount of error, the state equation can be obtained as follows:

{dot over (X)}=FX+W  (4.2)

In the above equation,

$\begin{matrix}{{F = \begin{bmatrix}0_{3 \times 3} & {f^{n} \times} & 0_{3 \times 3} & C_{b}^{n} \\0_{3 \times 3} & {{- \omega_{i\; ɛ}^{n}} \times} & {- C_{b}^{n}} & 0_{3 \times 3} \\0_{3 \times 3} & 0_{3 \times 3} & 0_{3 \times 3} & 0_{3 \times 3} \\0_{3 \times 3} & 0_{3 \times 3} & 0_{3 \times 3} & 0_{3 \times 3}\end{bmatrix}},{W = \begin{bmatrix}{C_{b}^{n}\nabla_{w}^{b}} \\{{- C_{b}^{n}}ɛ_{w}^{b}} \\0_{3 \times 1} \\0_{3 \times 1}\end{bmatrix}}} & (4.3)\end{matrix}$

In equation (4.3), ε_(w) ^(b) and ∇_(w) ^(b) are random white noises inthe body coordinate system (b system) of the accelerometer and gyroscoperespectively. Through test and verification, after comprehensivetemperature compensation and elimination of the Warm-up factor, theoutput of inertial instrument can be characterized as zero mean normaldistribution. In practical applications, an Allan variance is usuallyused to solve each model coefficient as the prior value of inertialinstrument model estimation.

${{f^{n} \times} = \begin{bmatrix}0 & {- g} & 0 \\g & 0 & 0 \\0 & 0 & 0\end{bmatrix}},$

g is the acceleration of gravity, ƒ^(n)=[0 0 g], x is defined as ananti-symmetric matrix formula, a vector is defined as H=[a b c], and itsanti-symmetric matrix is defined as

$\left( {H \times} \right) = {\begin{bmatrix}0 & {- c} & b \\c & 0 & {- a} \\{- b} & a & 0\end{bmatrix}.}$

When the GMD system is aligned under the static base, the body isstationary, and the output velocity v^(n) of the navigation solution isthe velocity error δv^(n). δv^(n) is used as the measurement data, andthe measurement equation is:

Z _(v) =δv ^(n) =H _(v) X+V _(v)  (4.4)

in which V_(v) is the velocity measurement noise in the navigationcoordinate system, δv^(n) is the velocity error, I represents the unitmatrix, and X represents the Kalman filter state variable; Z_(v) is avelocity observed value, H_(v)=[I_(3×3)0_(3×3)0_(3×3)0_(3×3)].

The theoretical analysis of observability of single-position Kalmanalignment is relatively mature. When Kalman optimal estimation alignmentmethod is adopted under a static base, the observability of Ø_(U), ε_(N)and ε_(U) is weak, while ∇_(E), ∇_(N) and ε_(E) are completelyunobservable. Single-position Kalman alignment under a static basecannot estimate the constant drift of the accelerometers in the east andnorth directions or error of the gyroscopes in the east direction.However, the error of the east accelerometer determines the misalignmentangle in the north direction, the error of the north accelerometerdetermines the misalignment angle in the east direction, and the azimuthmisalignment angle mainly depends on the error of the equivalent eastgyroscope. Therefore, under the condition of a static base, the initialalignment method of single-position Kalman optimal estimation isadopted. Because the observability of the core inertial instrument isweak, the accuracy of initial alignment is limited by the constant driftof the inertial instrument, while the convergence time of horizontalattitude alignment and the convergence time of azimuth alignmentrespectively depend on the random drift of the horizontal accelerometerand the angle random walk coefficient of the east gyroscope.

For directional drilling measurement applications, the accuracy of thecurrent high-temperature quartz flexible accelerometer can basicallymeet the requirements of attitude alignment accuracy under a staticbase, and the accuracy of the gyroscope, especially the repeatabilityerror of successive startup, has become the core factor restricting theazimuth alignment accuracy. There are many ways to improve the accuracyof azimuth measurement. On the one hand, one way is to improve theaccuracy of inertial instrument itself, and fundamentally solve thefactors affecting repeatability errors, such as precision machining ofsensing units of inertial instrument, static balance and dynamicbalance, optimization of material characteristics, optimization of thecontrol circuit, etc., but there are problems such as a long researchand development cycle and a high cost. On the other hand, from the pointof view of calibration, using the characteristics of current inertialinstruments, the purpose of improving the precision of inertial systemis achieved through external calibration or internal calibration, whileexternal calibration usually adopts the method of multi-positionindex+Kalman algorithm.

In essence, the two-position alignment method belongs to Euler angleinitial alignment under a static base, and the optimal estimation ofinertial instrument error cannot be realized by analyzing thetwo-position alignment, especially under the east-west well trajectory.It can be seen from FIG. 4 that the azimuth alignment accuracydeteriorates sharply when the inclination angle is greater than 10°. Inaddition, because the analytical method only picks up the outputinformation of inertial instruments on the body for a period of time asobservations, its alignment accuracy is limited by the ideal degree thatthe body is still without sloshing in the sampling period. Because theGMD works in the state of stopping drilling and finding north, the mudmotor may still work, and when the interference angular rate caused bymud sloshing is greater than the earth rotation angular rate, theanalytical two-position alignment cannot work normally. Kalmanmulti-position alignment based on optimal estimation has the ability offault tolerance of information and alignment under slight sloshing.Without changing the precision of inertial instrument itself, it ispossible to improve the observability of the errors of the inertialinstrument and realize the optimal estimation of inertial instrumenterrors, thus improving the initial alignment accuracy. Limited by thenarrow size of the probe, two-position change around the axial directionof the probe is the preferred solution of the present invention.

Similar to the state equation established for initial alignment ofKalman optimal estimation under a static base, the state equation oftwo-position Kalman optimal estimation is as shown in equation (4.2).Assuming that the position changing time is short, it is considered thatthe constant drift errors ε₀ ^(b) and ∇₀ ^(b) are fixed before and afterchanging the position, which is similar to the alignment of two-positionanalytical method. The attitude matrix C_(b) ^(n) of an inertialnavigation system is changed by external rotation, thus increasing theobservability of system state variables, especially the constant driftof the inertial instrument. The two-position method realizes precisealignment and estimates the error of the inertial instrument at the sametime. Similarly, when the rotation angle is 180°, the change of attitudematrix C_(b) ^(n) is the largest, and the observability of the estimatedstate is the strongest. Equations (4.5) and (4.6) are solved.

The equation of the attitude error of the GMD under a static base isshown in equation (4.5):

$\begin{matrix}{\left( \phi^{n} \right)^{T} = {{{{- \omega_{ie}^{n}} \times \left( \phi^{n} \right)^{T}} - {C_{b}^{n}\left( ɛ_{0}^{b} \right)}^{T} - {C_{b}^{n}\left( ɛ_{w}^{b} \right)}^{T}} = {{\left\lbrack \begin{matrix}0 & {\omega_{ie}\sin\; L} & {{- \omega_{ie}}\cos\; L} \\{{- \omega_{ie}}\sin\; L} & 0 & 0 \\{\omega_{ie}\cos\; L} & 0 & 0\end{matrix} \right\rbrack\begin{bmatrix}\phi_{E} \\\phi_{N} \\\phi_{U}\end{bmatrix}} - {C_{b}^{n}\begin{bmatrix}ɛ_{0x}^{b} \\ɛ_{0y}^{b} \\ɛ_{0z}^{b}\end{bmatrix}} - {C_{b}^{n}\begin{bmatrix}ɛ_{wx}^{b} \\ɛ_{wy}^{b} \\ɛ_{wz}^{b}\end{bmatrix}}}}} & (4.5)\end{matrix}$

The equation for the velocity error of a GMD under a static base isshown in equation (4.6):

$\begin{matrix}{\left( {\delta{\overset{.}{v}}^{n}} \right)^{T} = {{{f^{n} \times \left( \phi^{n} \right)^{T}} + {C_{b}^{n}\left( \nabla_{0}^{b} \right)}^{T} + {C_{b}^{n}\left( \nabla_{w}^{b} \right)}^{T}} = {{\begin{bmatrix}0 & {- g} & 0 \\g & 0 & 0 \\0 & 0 & 0\end{bmatrix}\begin{bmatrix}\phi_{E} \\\phi_{N} \\\phi_{U}\end{bmatrix}} + {C_{b}^{n}\begin{bmatrix}ɛ_{0x}^{b} \\ɛ_{0y}^{b} \\ɛ_{0z}^{b}\end{bmatrix}} + {{C_{b}^{n}\begin{bmatrix}ɛ_{wx}^{b} \\ɛ_{wy}^{b} \\ɛ_{wz}^{b}\end{bmatrix}}.}}}} & (4.6)\end{matrix}$

The best observation of ∇_(0x) ^(b) and ∇_(0y) ^(b), ε_(0x) ^(b) andε_(0y) ^(b) can be realized by changing the position by 180°. The formercan improve the estimation accuracy of Ø_(E) and Ø_(N), while the lattercan improve the estimation accuracy of Ø_(U). However, the observabilityof ∇_(Z) itself is high under a small inclination angle. Therefore, forthe solution of axially changing the position around a GMD probe, as thetraditional Kalman optimal estimation method of static base alignment,when only a velocity error δv^(n) is used for the observation equation,the observability of the Z-axis gyro drift ε_(z) is the worst, whichlimits the azimuth measurement accuracy when the GMD works at a largeinclination angle.

According to the azimuth measurement principle of the standard strapdowninertial navigation system in FIG. 18, when the position of the Z-axisis changed, according to the equations (3.5)-(3.9), the X-axis gyroscopeand the Y-axis gyroscope can separate the repeatability error by the wayof changing the position. However, when the well inclination angle islarge, especially in the east-west direction, the Z-axis gyroscopebecomes an/a east (west) gyroscope, and due to the size of the GMD, theposition changing mechanism can only rotate around the Z-axis.Therefore, the Z-axis gyroscope will not be able to separate the errorcoefficient by means of changing the position at a large wellinclination angle. At this time, if there is only zero-velocitycorrection, it is impossible to estimate the repeatability drift errorof the Z-axis gyroscope. According to equations (2.9), (2.10) and(2.11), the azimuth alignment accuracy mainly depends on the drift errorof the east gyroscope, while the drift error of the Z-axis gyroscopecannot be estimated at this time, therefore, the azimuth accuracy cannotmeet the requirements.

In order to estimate the constant drift error of the Z-axis gyroscopeunder a large well inclination angle, it is necessary to increase theobservations. In this text, the earth rotation angular rate under astatic base is used as a new observation. After obtaining the optimalestimation of the horizontal attitude, the difference between theprojection of a body coordinate system under a navigation system and theearth angular rate under the navigation system is used as Kalmanobservation information. Simulation shows that the drift error of theZ-axis gyroscope is well estimated.

The measurement equation is as follows:

Z _(ω)=δω^(n) ={tilde over (C)} _(b) ^(n){tilde over (ω)}^(b)−{tildeover (ω)}_(ie) ^(n)=(I−ϕ ^(n)×)C _(b) ^(n)(ω^(b)+ε^(b))≈(C _(b)^(n)ω^(b)×)ϕ^(n) +C _(b) ^(n)ε^(b)=ω_(ie) ^(n)×ϕ^(n) +C _(b)^(n)ε^(b)  (4.7)

The measurement equation obtained from this is:

Z _(ω)=[0_(3×3)ω_(ie) ^(n) ×C _(b) ^(n)0_(3×3)]X+V _(ω)  (4.8)

In equation (4.8), V_(ω) refers to the angular rate measurement noise,Z_(ω) represents an angular rate observation.

So far, a complete Kalman optimal estimation state equation (4.2) hasbeen established, and the measurement equations are as follows inequations (4.4) and (4.8).

Explanation of relevant meanings of this part:

For an error model of inertial instrument, under a static base, byignoring the scale factor error and installation error, an output modelof a gyroscope in a body coordinate system can be expressed as:

{tilde over (ω)}^(b)=ω^(b)+ε₀+ε_(r)+ε_(w)  (4.9)

where, {tilde over (ω)}^(b) is the average value of a sampling output ofthe gyroscope, ω^(b) is the true angular rate input value of thegyroscope, ε₀ is the constant drift of the gyroscope, ε_(r) is a slowdrift, and ε_(w) is a fast drift.

According to the Allan variance concept, ε₀ is mainly the repeatabilityerror of successive start-p, which can be expressed by a randomconstant, and its error model is:

{acute over (ε)}₀=0  (4.10)

The slow drift ε_(r) represents the trend term of the gyroscope andrepresents the rate ramp term in the Allan variance, which can usuallybe described by a first-order Markov process, namely:

$\begin{matrix}{{\overset{.}{ɛ}}_{r} = {{{- \frac{1}{\tau_{g}}}ɛ_{r}} + w_{r}}} & (4.11)\end{matrix}$

In equation (4.11), τ_(g) is the relevant time of the Markov process,and w_(r) is a white noise.

According to the Allan variance of a high-temperature gyroscopeprototype, through comprehensive error compensation, the trend termerror related with time of the gyroscope can be suppressed, and theAllan variance of the gyroscope can be kept for a long time after“bottoms out” time. Therefore, in fact, the Markov relevant time is longand can be ignored in alignment time, and the output model of thegyroscope can be simplified as:

{tilde over (ω)}^(b)=ω^(b)+ε₀+ε_(w)  (4.12)

where, the bias error of the gyroscope is:

ε=ε₀+ε_(w)  (4.13)

Usually, the term ε_(w) related to the white noise is expressed by anangle random walk coefficient ARW.

Similarly, the output model of the accelerometer can be simplified as:

{tilde over (ƒ)}^(b)=ƒ^(b)+∇₀+∇_(w)  (4.14)

where, {tilde over (ƒ)}^(b) is the mean value of a sampling output ofthe accelerometer, ƒ^(b) is the actual acceleration value of theaccelerometer, ∇₀ is the constant drift of the accelerometer and ∇_(w)is a random error of the white noise.

∇₀ is mainly the repeatability error of successive startup of theaccelerometer, which can also be expressed by a random constant, and itserror model is:

{dot over (∇)}₀=0  (4.15)

The bias error of the accelerometer is defined as:

∇=∇₀+∇_(w)  (4.16).

5. Flow Design of a Two-Position+Kalman Algorithm

The state equation (4.2) and measurement equations (4.4) and (4.8) arediscretized, and the state space model of a stochastic system alignedunder a GMD static base is obtained:

$\begin{matrix}\left\{ \begin{matrix}{X_{k} = {{\Phi_{{k/k} - 1}X_{k - 2}} + {\Gamma_{k - 1}W_{k - 1}}}} \\{Z_{k} = {{H_{k}X_{k}} + V_{k}}}\end{matrix} \right. & (5.1)\end{matrix}$

In equation (5.1), X_(k) is the 12×1-dimension state vector shown inequation (4.1) (in equation (4.1): δv^(n) is a velocity error, ϕ^(n) isa mathematical platform misalignment angle of strapdown inertialnavigation, ε₀ ^(b) is a high-temperature gyroscope constant drift and∇₀ ^(b) is a high-temperature accelerometer constant bias, each of whichcontains triaxial components, totaling 12), Z_(k) is a measurementvector composed of a velocity measurement Z_(v) and an angular ratemeasurement Z_(ω), Φ_(k/k-1) is the discretization of 12×1-dimensionone-step state transition matrix F, and Kalman is recursive. Therefore,k−1 is the last time, k is the one-step recursive time for k−1;Γ_(k/k-1) is a system noise distribution matrix, H_(k) is a measurementmatrix, W_(k-1) is a system noise vector, V_(k) is the measurement noisevector, including velocity measurement noise and angular ratemeasurement noise, and W_(k-1) and V_(k) are uncorrelated zero-meanGaussian white noise vector sequences, then:

E{W _(k) W _(j) ^(T) }=Q _(k)δ_(kj);  (5.2)

E{V _(k) V _(j) ^(T) }=R _(k)δ_(kj);  (5.2)

E{W _(k) V _(j) ^(T)}=0  (5.2)

Q_(k) and R_(k) are respectively called as variance matrices of a systemnoise and a measurement noise, which are required to be knownnon-negative definite matrix and positive definite matrix respectivelyin Kalman filter, and δ_(kj) is Kronecker δ function; when k≠j,δ_(kj)=0, and when k=j, δ_(kj)=1.

The discrete Kalman filter equation of GMD fine alignment can be dividedinto five basic formulas, as follows:

{circle around (1)} one-step state prediction equation

{circumflex over (X)} _(k/k-1)=Φ_(k/k-1) {circumflex over (X)}_(k-1/k-1)  (5.3)

{circle around (2)} one-step prediction mean square error equation

P _(k/k-1)=Φ_(k/k-1) P _(k-1/k-1)Φ_(k/k-1) ^(T)+Γ_(k/k-1) Q_(k-1)Γ_(k/k-1) ^(T)  (5.4)

{circle around (3)} filter gain equation

K _(k) =P _(k/k-1) H _(k) ^(T)(H _(k) P _(k/k-1) H _(k) ^(T) +R_(k))⁻¹  (5.5)

{circle around (4)} state estimation equation

{circumflex over (X)} _(k/k) ={circumflex over (X)} _(k/k-1) +K _(k)(Z_(k) −H _(k) {circumflex over (X)} _(k/k-1))  (5.6)

{circle around (5)} state estimation mean square error equation

P _(k/k)=(I−K _(k) H _(k))P _(k/k-1)  (5.7)

FIG. 7 is the flow chart of the Kalman filter algorithm. It can be seenfrom the figure that the algorithm flow of the Kalman filter can bedivided into two calculation loops and two update processes. The leftside is a filter calculation loop to complete the iterative calculationof the estimated state variable, and the right side is a gaincalculation loop to complete the calculation of Kalman gain. The upperand lower parts of the dotted line constitute two update processes.During the time update, the state one-step prediction {circumflex over(X)}_(k/k-1) and mean square error one-step prediction P_(k/k-1) arecompleted. After the time update is completed, if there is nomeasurement data at this time, the one-step prediction value is used asthe optimal estimation output of the state. In the position changingprocess of GMD, neither the velocity measurement with zero-speedcorrection nor the angular rate measurement constrained by the earthrotation angular rate is available, so there is no measurement data inthis process. The optimal estimation value is the one-step predictionvalue, i.e.: {circumflex over (X)}_(k)={circumflex over (X)}_(k/k-1) andP_(k)=P_(k/k-1). If the measurement data value is valid, that is, theGMD is in a static state before and after changing the position, and itis judged that the disturbance amount of the external mud is less thanthe set value, then the measurement update is started, the gaincoefficient K_(k) is calculated to obtain the optimal state estimation{circumflex over (X)}_(k/k), and the covariance matrix P_(k/k) at thistime is calculated. So far, a cycle of optimal state estimation has beencompleted.

A two-position alignment algorithm based on Kalman optimal estimationuses attitude update algorithm and velocity update algorithm of astrapdown inertial navigation to update angular motion and linear motionof the body in real time, and uses the zero-velocity and earth rotationangular rate correction algorithms for measurement update and optimalestimation. Therefore, the optimal estimation accuracy is irrelevant tothe accuracy of changing the position, and there is no need to know theexact position of the position changing mechanism, which is verybeneficial in engineering practice, thereby avoiding the design of acomplex stop structure and further avoiding the use of high-temperatureresistant angle measuring mechanism. This is the characteristic andadvantage of the Kalman algorithm+two position alignment method of thepresent invention.

In the process of measurement update, it is necessary to solve theinverse operation of a high-dimensional matrix, so as to obtain the gaincoefficient of Kalman filter. In order to reduce the computation,Sequential Kalman Filter is often used to solve the measurement matrixcomposed of velocity measurement Z_(v) and earth rotation angular ratemeasurement X_(ω).

The flow of GMD two-position fine alignment using sequential processingis shown in FIG. 8. The effective interpretation of Z_(k) in FIG. 8 isto judge the validity of the measurement data (equations (4.4) and(4.8)), that is, to set the criteria of sensing velocity or sensingangular rate to judge whether the drill collar is in a static state orwhether to ensure that its slight disturbance does not affect thealignment accuracy. After updating the state variables, when the GMDprobe is in a static or slightly disturbed state, whether theobservation is valid or not is automatically judged by the collecteddata of accelerometer and gyroscope in a period of time, and thevelocity measurement Z_(v) update and angular rate measurement Z_(ω)update are respectively completed according to sequential processing,and the Kalman gain is calculated to achieve the optimal estimation ofconstant drift errors of X and Y horizontal gyroscopes and estimation ofthe constant drift error of the Z-axis gyroscope (the optimal estimationof constant drift error of the gyroscopes is reflected in drift errorsof ε₀ ^(b) and ∇₀ ^(b) of gyroscopes and accelerometers contained instate matrix X), and finally complete the optimal estimation of theattitude and azimuth misalignment angle.

The final result of the optimal estimation under the valid measurementequation is equation (5.6), and equation (5.7) is the evaluation ofestimation effect after estimation. Equations (5.3) to (5.7) are anestimation process and a recursive process.

After GMD system detects the instruction of stopping drilling andfinding north, it starts the mode of finding north (initial alignment).The basic flow of Kalman two-position alignment algorithm is as follows:

1) at the initial position 1, completing the coarse alignment within 20s by adopting an analytical coarse alignment algorithm,

2) taking the horizontal attitude angle and azimuth angle after thecoarse alignment as the initial values of Kalman filter, carrying out130 s of fine alignment and drift measurement of the inertial instrumentat position 1, estimating the inertial instrument error and misalignmentangle error, and then entering the navigation state with the results ofthis alignment as the initial values,

in East-North-Up geographic coordinate system, the defined horizontalattitude angles, i.e., the pitch angle and roll angle, correspond to thewell inclination angle and tool face angle for drilling measurement. Thedefined azimuth angle, i.e., the azimuth angle in East-North-Upgeographic coordinate system, corresponds to the azimuth angle and theincluded angle between the geographical north direction therebetween indrilling measurement terms,

3) on the premise of ensuring that the position changing angular rate isless than the maximum measuring range of the Z-axis gyroscope,completing the position change by 180° within 20 s, changing to position2, and updating the attitude and velocity navigation data at the sametime, 180° is preferred, but the present invention is not onlyapplicable to the position change by 180°, but to arbitrary position,

4) carrying out of fine alignment at position 2 for 130 s, estimatingthe horizontal attitude and azimuth error angle and completing the driftmeasurement of the inertial instrument, there are many ways to realizedrift measurement in this field, which will not be repeated here.

The whole alignment process can be completed in about 300 s, and theflow is shown in FIG. 9.

The process of the fine alignment is as follows:

Step 1: the attitude update and velocity update are performed,

taking the pitch angle, roll angle and yaw angle (corresponding to thewell inclination angle, tool face angle and azimuth angle in drilling)of the coarse alignment as initial values, adopting the navigationalgorithm to update the velocity and attitude.

1.1 the algorithm for attitude update is as below:

In order to understand attitude update and velocity update more simply,the basic algorithms are listed here. In fact, as a navigationalgorithm, attitude update and velocity update belong to the prior art,and the general physical and mathematical methods are given here:

A quaternion method: quaternion is a mathematical method, which is usedas a convenient tool for describing coordinate system transformationrelationship and solving an attitude matrix in a strapdown inertialnavigation system.

According to Euler's one-rotation theorem when a rigid body moves arounda fixed point, the limited rotation of a rigid body from one position toanother can be realized by one rotation by a certain angle around anaxis passing through the fixed point, and the one rotation can beexpressed by the following unit quaternion:

$q = {{{\cos\frac{\alpha}{2}} + {{\xi sin}\frac{\alpha}{2}}} = {q_{0} + {q_{1}i_{b}} + {q_{2}j_{b}} + {q_{3}k_{b}}}}$

The angle α in q in a quaternion represents the angle of one rotation,the vector ξ represents the azimuth of the rotating axis of onerotation, and the direction of ξ is taken as the positive direction ofthe rotation angle α according to the right-hand rule.

The relationship between the quaternion and attitude matrix C_(b) ^(n)is:

$\begin{matrix}{C_{b}^{n} = \begin{bmatrix}{q_{0}^{2} + q_{1}^{2} + q_{2}^{2} + q_{3}^{2}} & {2\left( {{q_{3}q_{2}} - {q_{0}q_{3}}} \right)} & {2\left( {{q_{0}q_{2}} + {q_{1}q_{3}}} \right)} \\{2\left( {{q_{0}q_{2}} + {q_{0}q_{3}}} \right)} & {q_{0}^{2} - q_{1}^{2} + q_{2}^{2} - q_{3}^{2}} & {2\left( {{q_{2}q_{3}} - {q_{0}q_{1}}} \right)} \\{2\left( {{q_{1}q_{3}} - {q_{0}q_{2}}} \right)} & {2\left( {{q_{0}q_{1}} + {q_{2}q_{3}}} \right)} & {q_{0}^{2} - q_{1}^{2} - q_{2}^{2} + q_{3}^{2}}\end{bmatrix}} & (a)\end{matrix}$

Therefore, given the quaternions q₀, q₁, q₂ and g₃ of rotation of abody, the transition matrix C_(b) ^(n) from a body coordinate system toa navigation coordinate system can be obtained, thus the navigationcalculation of the strapdown inertial navigation system can be carriedout.

The quaternion differential equation is established by the angular rate{tilde over (ω)}^(b) measured by the body coordinate system b system:

{dot over (q)}(t)=½q(t)·{tilde over (ω)}^(b)  (b)

The quaternion can be obtained by obtaining the angular rate vector ofthe body in real time, and the attitude and azimuth information, θ, γand φ, of the body can be obtained according to formula (a).

When solving formula (b), it is a differential equation, and it isnecessary to obtain the initial values of the quaternion, i.e., q₀(0),q₁(0), q₂(0) and q₃(0). The initial values of azimuth and attitudeobtained by coarse alignment are defined as: θ₀, γ₀ and φ₀.

The initial quaternion can be obtained as follows:

$\begin{bmatrix}{q_{0}(0)} \\{q_{1}(0)} \\{q_{2}(0)} \\{q_{3}(0)}\end{bmatrix} = \begin{bmatrix}{{\cos\frac{\theta_{0}}{2}\cos\frac{\varphi_{0}}{2}\cos\frac{\gamma_{0}}{2}} + {\sin\frac{\theta_{0}}{2}\sin\frac{\varphi_{0}}{2}\sin\frac{\gamma_{0}}{2}}} \\{{\cos\frac{\theta_{0}}{2}\cos\frac{\varphi_{0}}{2}\sin\frac{\gamma_{0}}{2}} - {\sin\frac{\theta_{0}}{2}\cos\frac{\varphi_{0}}{2}\cos\frac{\gamma_{0}}{2}}} \\{{\cos\frac{\theta_{0}}{2}\cos\frac{\varphi_{0}}{2}\cos\frac{\gamma_{0}}{2}} + {\sin\frac{\theta_{0}}{2}\cos\frac{\varphi_{0}}{2}\sin\frac{\gamma_{0}}{2}}} \\{{\sin\frac{\theta_{0}}{2}\cos\frac{\varphi_{0}}{2}\cos\frac{\gamma_{0}}{2}} - {\cos\frac{\theta_{0}}{2}\cos\frac{\varphi_{0}}{2}\sin\frac{\gamma_{0}}{2}}}\end{bmatrix}$

By recursively solving the quaternion differential equation (b), thequaternion of the body can be obtained and updated continuously, so asto obtain the attitude transition matrix of the body and calculate theattitude and azimuth information, θ, γ and φ, of the body in real time.

The body here is the drill collar assembly that needs to be measured bya GMD.

1.2 The velocity update algorithm is:

the velocity differential equation, i.e., the specific force equation,is the basic relational expression of an inertial navigation solution:

{dot over (v)} ^(n) =C _(b) ^(n)ƒ^(b)−(2ω_(ie) ^(n)+ω_(εn) ^(n))×v ^(n)+g ^(n)  (5.8)

where, g^(n)=[0 0−g]^(T), which is the projection of acceleration ofgravity in a navigation coordinate system.

In the equation, ƒ^(b) refers to the three-component value of the bodycoordinate system of b system measured by an accelerometer in real time.In equation (5.8), all parameters are vectors.

ω_(ib) ^(b) indicates the component of the rotational angular rate ofthe b system relative to the i system in the b system, ω_(in) ^(n)indicates the component of the rotational angular rate of the n systemrelative to the i system in the n system, and

$\omega_{ie}^{n} = \begin{bmatrix}0 & {\omega_{ie}\cos\; L} & {\omega_{ie}\sin\; L}\end{bmatrix}^{T}$ $\omega_{ɛ\; n}^{n} = \begin{bmatrix}{- \frac{v_{N}}{R_{M} + h}} & \frac{v_{E}}{R_{N} + h} & \frac{v_{N}\tan\; L}{R_{N} + h}\end{bmatrix}^{T}$

where, v_(E) and v_(N) are east and north velocities, L and h arelatitude and height;

ω_(ie) is the angular rate of the earth rotation.

Given the latitude L, the meridian circle curvature radius R_(M) andprime vertical circle curvature radius R_(N) can be calculated asfollows:

${R_{M} = \frac{{R_{e}\left( {1 - f} \right)}^{2}}{\left\lbrack {1 - {\left( {2 - f} \right)f\;\sin^{2}L}} \right\rbrack^{\frac{3}{2}}}},{R_{N} = {\frac{R_{e}}{\left\lbrack {1 - {\left( {2 - f} \right)f\;\sin^{2}L}} \right\rbrack^{\frac{1}{2}}}.}}$

The oblateness ƒ is defined by China Geodetic Coordinate System 2000(CGCS2000) ellipsoid standard or World Geodetic System-1984 CoordinateSystem (WGS-84) ellipsoid standard.

Step 2, Kalman filter is carried out, the specific algorithm is dividedinto two parts: time update and measurement update.

2.1 Attitude update: the quaternion updated in the attitude updatealgorithm of 1.1 is substituted into the attitude transition matrixC_(b) ^(n) to update the F matrix and W matrix in the Kalman stateequation (4.2), thus realizing the attitude update of Kalman.

The b system is fixedly connected with an IMU and rotates with the body.The origin is located at the sensing center of the position of the IMU,which is expressed by ox_(b)y_(b)z_(b), and the angular positionrelationship between b system and n system is expressed by an attitudematrix C_(n) ^(b). The attitude transition matrix of a navigationcoordinate system and a body coordinate system is as follows:

$C_{b}^{n} = \left\lbrack \begin{matrix}{{\cos\;{\psi cos\gamma}} + {\sin\;{\psi sin\theta sin\gamma}}} & {\sin\;{\psi cos\theta}} & {{\cos\;{\psi sin\gamma}} - {\sin\;{\psi sin\theta cos\gamma}}} \\{{{- \sin}\;{\psi cos\gamma}} + {\cos\;{\psi sin\theta sin\gamma}}} & {\cos\;{\psi cos\theta}} & {{- {\psi sin\theta sin\gamma}} - {\cos\;{\psi sin\theta cos\gamma}}} \\{{- \cos}\;{\theta sin\gamma}} & {\sin\;\theta} & {{- \cos}\;{\theta sin\gamma}}\end{matrix} \right\rbrack$

2.2 Time update: the specific update equations are one-step stateprediction equation and one-step prediction mean square error equation;

One-step state prediction equation (5.3):

{circumflex over (X)} _(k/k-1)=Φ_(k/k-1) {circumflex over (X)}_(k-1/k-1),

One-step prediction mean square error equation (5.4):

P _(k/k-1)=Φ_(k/k-1) P _(k-1/k-1)Φ_(k/k-1) ^(T)+Γ_(k/k-1) Q_(k-1)Γ_(k/k-1) ^(T),

Φ_(k/k-1) is the discretization of the 12×1-dimension one-step statetransition matrix F, and Γ_(k/k-1) is a system noise distributionmatrix.

Time update is only an update of 12 state variables of calculation statevariables under the real-time data collected by different gyroscopes andaccelerometers, but the measurement data is not used at this time.Measurement update is to use the measurement data to correct the errorof state update and realize the optimal estimation (azimuth andhorizontal attitude, drifts of the gyroscope and accelerometer, i.e., 9of 12 variables).

2.3 Measurement update:

2.3.1 Firstly, a criterion is set to judge whether the measurement datavalue is valid. The validity of the measurement data value can be judgedby judging whether the drill collar is in a static state or whether theexternal disturbance does not affect the alignment accuracy. Only whenthe measurement data value is valid, measurement update is carried out;otherwise, measurement update is not carried out, but only time updateis carried out. That is, the update result of one-step state predictionequation or one-step prediction mean square error equation in the timeupdate is taken as the output of Kalman filter (that is, the horizontalattitude information and azimuth information at this time are outputfrom equation (5.3)/(5.4)). The setting for judging whether the drillcollar is in a static state can be as follows: the observed sensingvelocity observation (such as an acceleration value) or sensing angularrate observation (such as a root mean square value of the gyroscopeangular rate) is set, and when the value is less than a certain value,measurement update is carried out. If always unsatisfied, no measurementupdate will be made, only time update will be made. The criterion ofexternal disturbance can be whether the external mud disturbance or themeasured value of a vibration sensor is less than the set threshold. Ifso, the alignment accuracy is not affected and the measurement isupdated; otherwise, the measurement update is not made but only the timeupdate is made.

2.3.2 Measurement update

Measurement equations (4.4) and (4.8) are a velocity measurement basedon zero-velocity constraint and an angular rate measurement based onearth rotation angular rate constraint respectively.

The two kinds of measurements are subject to sequential processing, thatis, the measurement update equations (i.e., equations (5.5), (5.6) and(5.7)) are executed respectively.

The state estimation equation (5.6) is the final optimal estimatedKalman filter value, which includes the mathematical platformmisalignment angle Ø^(n) of the strapdown inertial navigation, the gyroconstant drift ε₀ ^(b) and the accelerometer constant bias ∇₀ ^(b).Equation (5.7) is the evaluation of estimation effect after estimation.

6: Simulation Test and Analysis of the Two-Position Kalman AlignmentAlgorithm

The initial position is set as [116° E, 40° N, 100 m]. The parameters ofa high-temperature inertial instrument are shown in Table 1. Thesimulation process is the same as the analytical two-position alignmentmethod. In a well inclination angle of 0-90°, one position is taken forsimulation at every 5°. There are 19 positions in total. 40 Monte-Carlosimulations are performed at each position and the root mean squarevalue is taken. The simulated well trajectory direction is divided intosouth-north direction and east-west direction. The azimuth alignmenterror under different well inclination angles and the ability ofinertial instrument to measure a drift are analyzed.

Simulation 1: the well trajectory is south-north direction, and thevertical well attitude is [0°,0°,0°] and the horizontal well attitude is[90°,0°,0°] in the geographic coordinate system. FIG. 10 is a curve ofmisalignment angle errors, and FIG. 11 is the constant drift estimationerrors of the gyroscope and accelerometer respectively.

It can be seen from FIG. 10 that the azimuth measurement accuracyremains basically unchanged under different well inclination angles forthe well trajectory in the south-north direction, and the relatedmechanism analysis is similar to the analytical two-position alignment,that is, the horizontal-axis gyroscope can always be modulated by theposition changing mechanism in the south-north direction, and itsconstant drift can always be observed, and the azimuth alignmentaccuracy mainly depends on the angular random walk of the gyroscope. 40Monte-Carlo simulations are carried out at each position in FIG. 10, andthe root mean square value is taken. The standard deviation of anazimuth misalignment angle σ3 aligned in a full attitude from a verticalwell to a horizontal well is calculated as 0.0576°, which fully meetsthe design requirement for azimuth measurement accuracy of 1°.

Simulation 2: the well trajectory is east-west direction, with avertical well attitude [0°, 0°, 90°] and a horizontal well attitude[90°, 0°, 90°] in the geographic coordinate system. The followingsimulations of alignment accuracy and drift measurement ability arecarried out respectively under situations of a vertical section, a smallwell inclination angle and a large well inclination angle, and finallythe simulation conclusions of alignment accuracy and drift measurementability under different well inclination angles and different directionsare obtained.

1) In a simulation analysis of a vertical well section, an initialattitude angle is set as [0°,0°,90°]

FIG. 12 is a curve of simulated misalignment angles, and FIG. 13 is acurve of constant drift estimation errors of an accelerometer (b) and agyroscope (a). After changing the position by 180°, the constant drifterror of inertial instrument is quickly eliminated, thus eliminating thealignment error between the horizontal attitude and azimuth. The finalsimulation results show that the final azimuth misalignment angleestimation error is −0.1°, and the misalignment angle is only related tothe random drift error of the inertial instrument.

2) Simulation analysis of an east-west inclined well section

In the simulation experiment of a two-position analytical alignment,FIG. 4 shows that when the well inclination angle is greater than 10°,the accuracy error of azimuth alignment exceeds the design index of 1°.In this simulation, a small well inclination angle of 15°, i.e., aninitial attitude angle of [15°, 0°, 90°], and a large well inclinationangle of 70°, i.e., an initial attitude angle of [70°, 0°, 90°], are setrespectively. The results of 20 Monte-Carlo simulation are shown inFIGS. 14(a) and 14(b).

It can be seen from FIG. 14 that, regardless of a small well inclinationangle or a large well inclination angle, the attitude and azimuthmisalignment angle errors can converge rapidly after changing theposition by 180°. At a small well inclination angle of 15°, the azimuthmisalignment angle average value at the end of alignment is −0.0072° andthe standard deviation value of 3σ is 0.4°, and at a large wellinclination angle of 70°, the azimuth misalignment angle average valueat the end of alignment is 0.1° and the standard deviation value of 3σis 0.9°, both of which meet the azimuth accuracy requirement of 1°.

FIGS. 15(a) and 15(b) show a simulation result of inertial instrumentdrift estimation at a large well inclination angle of 70°. When thefinal alignment is finished, the constant drift estimation error of thegyroscope (corresponding to FIG. 15(a)) is [0.01, −0.02, −0.05] deg/h,and the constant drift estimation error of the accelerometer(corresponding to FIG. 15(b)) is [4.6, −0.5, −0.05] ug. At a large wellinclination angle of 70°, the constant drift of inertial instruments canstill be accurately estimated by Kalman optimal estimation. Therefore,the algorithm designed in this text can still achieve an azimuth errorless than 1° in the east-west direction at a large inclination of 70°under the condition that the current high-temperature gyroscope has arepeatability error of 2°/h.

3) in the azimuth accuracy analysis under a full well inclination angle,the well inclination angle is set to be in a range of 0-90° for thestimulation, and the simulation is performed every 5° of the wellinclination angle, each position includes 40 Monte-Carlo simulations,and the root mean square values of data of 40 azimuth misalignmentangles are taken at the end of alignment.

It can be seen from FIG. 16 that by adopting the optimal estimation oftwo-position Kalman+velocity measurement based on zero velocity andangular rate measurement based on earth rotation angular rate constraintproposed in this text, azimuth alignment accuracy better than 1° can bemaintained when the well inclination angle is less than 70° in east-westwell trajectory condition, and azimuth measurement accuracy better than5° can be achieved in a whole horizontal well section, and the resultsare far better than that of the two-position analytical method shown inFIG. 4.

It can also be seen from FIG. 17 that the drift error of a Z-axisgyroscope can guarantee an estimation accuracy of better than 0.2 deg/hin a vertical well section (0°) to the east-west large well inclinationangle (75°), and the estimation accuracy deteriorates when the drifterror is close to the horizontal well (90°), but estimation accuracy of1 deg/h can also be guaranteed. Therefore, the method of the presentinvention can well estimate the drift error of the X/Y gyroscope fromthe vertical well section to the horizontal well section, and cansatisfy the drift error estimation accuracy of the Z-axis gyroscope at alarge well inclination angle in the east-west horizontal well direction.

The alignment method of multi-position+position changing strapdownsolution+Kalman+velocity measurement after zero-speed correction andangular rate measurement constrained by the earth rotation angular rateis particularly suitable for a strapdown inertial navigation systemadopting a Coriolis vibratory gyroscope. The accuracy of the Coriolisvibratory gyroscope mainly depends on the processing accuracy, isotropyuniformity and control circuit accuracy of the resonator. However, dueto the actual influence of processing technology, the processingaccuracy and material uniformity of the resonator cannot reach theperfect level, which will inevitably lead to the angular rate estimationerror of the resonator gyroscope and the azimuth alignment error of thestrapdown inertial navigation system. According to the method providedby the present invention, aiming at the drift error of gyroscopes,especially Coriolis vibratory gyroscopes, the velocity measurement afterzero-speed correction and the angular rate measurement constrained bythe earth rotation angular rate are adopted for measurement update, andthe strapdown solution algorithm in the position changing process iscombined, so that the optimal estimation of the drift error of thegyroscope can be realized, and the azimuth measurement accuracy of theGMD system is improved.

The method of the present invention is applied to an inertial navigationsystem, and the inertial navigation system includes a triaxialgyroscope, a triaxial accelerometer and a shock absorber, wherein thegyroscope is fixedly connected with the shock absorber, the triaxialgyroscope is arranged at 90 degrees or other angles to each other. Theinertial navigation system is a strapdown inertial navigation system.

An application of the attitude measurement method is to apply themeasurement method to the north-finding process of a Coriolis vibratorygyroscope to realize the initial alignment of the gyroscope. TheCoriolis vibratory gyroscope applied in a Measurement While Drilling(MWD) system.

The attitude measurement method of the present invention can also beapplied to a multi-point gyrocompass measurement while drilling systemor a multi-point gyrocompass cable measurement system or a continuousnavigation measurement system with the capability of zero-speedcorrection to realize the attitude measurement of underground wells.

The attitude measurement method provided by the embodiment of thisapplication is described in detail above. The description of the aboveembodiments is only to facilitate understanding the method and its coreidea of the application; at the same time, according to the idea of thisapplication, there will be some changes in the specific implementationand application scope for those skilled in the art. To sum up, thecontents of this description should not be construed as limitations ofthis application. As “comprising” and “including” mentioned in the wholedescription and claims are open terms, they should be interpreted as“comprising/including but not limited to”. “Roughly” means that withinan acceptable error range, those skilled in the art can solve thetechnical problem within a certain error range and basically achieve thetechnical effect. It should be understood that the term “and/or” used inthis text is only a description of the association relationship ofassociated objects, which means that there can be three kinds ofrelationships, for example, A and/or B, which can mean that A existsalone, A and B exist at the same time, and B exists alone. In addition,the character “/” in this text generally indicates that the contextobject is an “or” relationship.

The above description shows and describes several preferred embodimentsof the application. It should be understood that the application is notlimited to the form disclosed herein, and should not be regarded as anexclusion of other embodiments, but can be used in various othercombinations, modifications and environments, and can be modified by theabove teaching or the technology or knowledge in relevant fields withinthe scope of the application conception described herein. However, themodifications and changes made by those skilled in the art do not departfrom the spirit and scope of this application, and should be within theclaimed scope of the appended claims of this application.

1. An attitude measurement method, used for a strapdown inertialnavigation system, wherein repeatability drift of a gyroscope issuppressed by adopting a method of performing fine alignment at aplurality of positions respectively; the method comprises the steps of:S1, taking current attitude data and velocity data of the strapdowninertial navigation system, and performing first fine alignment at afirst position; S2, changing the position of the strapdown inertialnavigation system to an nth position, and performing attitude update andvelocity update according to a result of an (n−1)th fine alignment in aposition changing process; and S3, taking results of the attitude updateand velocity update as nth initial values, and performing an nth finealignment at the nth position to complete an initial alignment of thestrapdown inertial navigation system; wherein, n is incremented by 1from 2, and steps S2 and S3 are repeated until n=k; k is the number ofpositions selected by the method, and k is greater than or equal to 2;wherein the plurality of positions are specifically two positions, i.e.,k=2.
 2. (canceled)
 3. The attitude measurement method according to claim1, wherein the fine alignment is realized by Kalman algorithm.
 4. Theattitude measurement method according to claim 3, wherein the finealignment using the Kalman algorithm comprises: time update and/ormeasurement update; the time update refers to completing update of astate variable according to real-time data collected by the system,including attitude update and velocity update; the measurement updaterefers to correcting an error of a state update with measurement data torealize optimal estimation; Kalman filter uses a velocity measurementafter zero-speed correction and an angular rate measurement constrainedby the earth rotation angular rate for the measurement update andoptimal estimation, so as to eliminate a drift error of the gyroscope.5. The attitude measurement method according to claim 4, wherein themeasurement update comprises the steps of: 1) judging whether ameasurement data value is valid, if the measurement data value is valid,entering step 2), otherwise, performing no update, and taking a resultof the time update as a final result of the Kalman filter; and 2)updating a result of the state update according to the measurement datavalue, calculating a gain coefficient according to an updating resultand the result of the time update to obtain optimal state estimation. 6.The attitude measurement method according to claim 5, wherein judgingwhether the measurement data value is valid is realized by judgingwhether a drill collar is in a static state and/or whether externaldisturbance meets an alignment requirement; if the drill collar is inthe static state and/or the external disturbance meets the alignmentrequirement, it is determined that the measurement data value is valid,otherwise, it is determined that the measurement data value is invalid.7. The attitude measurement method according to claim 6, wherein judgingwhether the drill collar is in the static state specifically comprises:judging whether a sensing-velocity observation value and/or asensing-angular-rate observation value is less than a judgmentthreshold; if the sensing-velocity observation value and/or thesensing-angular-rate observation value is less than the judgmentthreshold, judging that the drill collar is in the static state;otherwise, judging that the drill collar is not in the static state. 8.The attitude measurement method according to claim 6, wherein, judgingwhether the external disturbance meets the alignment requirementspecifically comprises: judging whether a disturbance amount of externalmud or a vibration amount sensed by a vibration sensor is less than aset threshold value; if the disturbance amount of external mud or thevibration amount sensed by the vibration sensor is less than the setthreshold value, judging that the external disturbance amount meets thealignment requirement, otherwise, judging that the external disturbanceamount does not meet the alignment requirement.
 9. The attitudemeasurement method according to claim 5, wherein the step 2)specifically comprises: respectively solving a measurement matrixcomposed of a velocity measurement Z_(V) after zero-speed correction andan angular rate measurement Z_(ω) constrained by the earth rotationangular rate, so as to realize constant drift error optimal estimationof X and Y horizontal gyroscopes and constant drift error estimation ofa Z-axis gyroscope, and finally complete optimal estimation of anattitude and azimuth misalignment angle.
 10. The attitude measurementmethod according to claim 4, wherein one-step state prediction andone-step mean square error prediction are completed during the timeupdate.
 11. The attitude measurement method according to claim 4,wherein the attitude update in the position changing process is carriedout by a quaternion method.
 12. The attitude measurement methodaccording to claim 1, wherein the measurement method further comprisesperforming coarse alignment at the first position, and performing thefirst fine alignment using a result of the coarse alignment as the firstinitial values.
 13. A measurement while drilling system, comprising astrapdown inertial navigation system which comprises a triaxialgyroscope and a triaxial accelerometer; wherein the strapdown inertialnavigation system adopts an attitude measurement method according toclaim 1, to suppress a repeatability drift error of the gyroscope andimprove accuracy of measurement while drilling in directional drilling.14. A continuous navigation measurement system, comprising a strapdowninertial navigation system which comprises a triaxial gyroscope and atriaxial accelerometer; wherein the strapdown inertial navigation systemadopts an attitude measurement method according to claim 1, to suppressa repeatability drift error of the gyroscope and improve attitudemeasurement accuracy in a navigation process.